Plurisubharmonic functions and Kählerian metrics on complexification of symmetric spaces
Plurisubharmonic functions and Kählerian metrics on complexification of symmetric spaces
复制标题
DOI：
10.1016/0019-3577(92)90017-f
复制
发表时间：
1992-12
期刊：
影响因子：
--
通讯作者：
H. Azad;J. Loeb
中科院分区：
文献类型：
--
作者：
H. Azad;J. Loeb
环k上的完全退化对称矩阵u通过超平面的识别得到了IP；xk上的正则等价关系，见第一节。商A，是稳定的拟阿贝尔格式。它是g维代数环面(.Ek Xk上k。在这个注记中，它被描述为投影R，其中R是关于u的完全退化的theta函数的正则分次环。R的显式知识为研究完全退化曲线的三分式提供了一个起点，其中u是曲线的周期矩阵，见[G]，0 1。在完全退化的情况下有机会检验三分式猜想。如果k=C，这个商A被Mumford认为是解析空间。它也是纳米卡瓦研究的稳定的准阿贝尔品种家族中的一种特殊纤维。IV.泛阿贝尔簇的紧化的一般问题在[FC]，第一章中讨论。在第一节中，描述了由u诱导的等价关系7。第二节介绍了多重齐次多项式的表示法。第三节研究了完全退化的theta多项式分次环R。在(3.4)中得到了R的r次齐次元的模R的一个基。从(3.6)得到A是射影的，从(3.7)得到正则映射P：xk-f A，是有限的。
A totally degenerate symmetric matrix u over a ring k gives rise to canonical equivalence relation on IP; xk by identification of hyperplanes, see Section 1. The quotient A, is a stable quasi-abelian scheme. It is a non-normal compactification of the g-dimensional algebraic torus (. Ek xk over k. In this note it is described as Proj R where R is a canonical graded ring of totally degenerate theta functions relative to u. The explicit knowledge of R provides a point of departure for studying the trisecant formula for totally degenerate curve where u is a period matrix of the curve, see [G], 0 1. There is a chance to test the trisecant conjecture in the totally degenerate case. If k= C this quotient A, was considered as analytic space by Mumford,[Ml, Chap. III b, 5 5. It also appears as a special fiber in the family of stable quasiabelian varieties studied by Namikawa,[N], Chap. IV. The general problem of the compactification of the universal abelian variety is discussed in [FC], Chap. VI, 5 1.In Section 1 the equivalence relation 7 induced by u is described. In Section 2 notations about multi-homogenous polynomials are introduced. The graded ring R of totally degenerated theta polynomials is studied in Section 3. In (3.4) a base for the module R, of homogenous elements of R of degree r is obtained. From (3.6) one gets that A, is projective and from (3.7) one gets that the canonical mapiP: x k---f A, is finite.